Advertising click-through rate (CTR) prediction is a fundamental task in recommender systems, aimed at estimating the likelihood of users interacting with advertisements based on their historical behavior. This prediction process has evolved through two main stages: from traditional shallow interaction models to more advanced deep learning approaches. Shallow models typically operate at the level of individual features, failing to fully leverage the rich, multilevel information available across different feature sets, leading to less accurate predictions. In contrast, deep learning models exhibit superior feature representation and learning capabilities, enabling a more realistic simulation of user interactions and improving the accuracy of CTR prediction. This paper provides a comprehensive overview of CTR prediction algorithms in the context of recommender systems. The algorithms are categorized into two groups: shallow interactive models and deep learning-based prediction models, including deep neural networks, convolutional neural networks, recurrent neural networks, and graph neural networks. Additionally, this paper also discusses the advantages and disadvantages of the aforementioned algorithms, as well as the benchmark datasets and model evaluation methods used for CTR prediction. Finally, it identifies potential future research directions in this rapidly advancing field.